I would keep the dvd rom and floppy (I only needed a floopy once for my cab and didnt have one, so had to rip one out of another computer to use for 5 minutes, but i wish woulda spent the $8-10 for one).
You might be able to get away with a cheaper sound card. Do you plan on using more than 2 speakers or 2 + a sub? Many older games are mono.
You can get a cheap ATI card off ebay, I paid $6 for mine (8MB card with s-video out) and it works great. You dont need anything fancy.
Speakers again, look for used stuff, ebay has lots, or garage sales. Ditto for ethernet cards.
You didnt say if you needed a motherboard/processor or not. If you do, there are some good deals for cheap available if you keep your eyes open. Last week Fry's had a sale on an ECS motherboard(K7S5A)& Athlon 2000+ package for $69. Not the best/most modern setup, but more than adequate for a mame cabinet, and cheap.
As for cooling, just make sure your cabinet has adequate venting and you should be ok. My cabinet is in my basement which is pretty cool, so I dont need a fan inside my cabinet, it never gets that warm. If you need a fan for airflow, consider using 12"+ oscilating fan or desk fan from wal-mart or someplace inside your cabinet. They are super cheap, quiet, and move alot of air. You can set them to not oscilate and just blow where you want. No one will see it since its hidden in your cabinet.
27" TV, I have a toshiba as do some other people here. Toshiba has some nice features, small case for a 27", remembers power state and settings when unplugged (so you can leave it on and set to s-video and unplug/shut off power bar and then plug in again and it turns on set to s-video). I got mine used, look around, pawn shops, garage sales, moving sales, local paper or forsale newsgroups.
Good luck.